The influence of response styles has become an essential topic in psychological assessment and educational measurement, and different approaches have been proposed to control for biasing effects of response styles in rating data. Here we present two prominent psychometric approaches that can be used to account for response styles: (a) multidimensional extensions of ordinal IRT models, and (b) IRTree models for polytomous item responses. We demonstrate how multidimensional IRT and IRTree models can be specified to capture various kinds of response styles, and we illustrate the two model families with data from the background questionnaire of the PISA 2018 study using the open-source statistical software R. The empirical application shows tha...